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Maths-

SAT

Easy

Question

The scatterplot above represents the salary y, in thousands of dollars, and the number of years of experience, x, for each of six employees at a company. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

$y = \frac{3}{2} x$
$y = \frac{3}{2} x + \frac{95}{2}$
$y = \frac{2}{3} x + \frac{95}{2}$
$y = \frac{2}{3} x + 55$

The correct answer is: $y equals 3 over 2 x plus 95 over 2$

The line contains points (1,49) & (5,55)
The line equation is
$fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction equals fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction$
$fraction numerator y minus 49 over denominator 55 minus 49 end fraction equals fraction numerator x minus 1 over denominator 5 minus 1 end fraction$
$fraction numerator y minus 49 over denominator 6 end fraction equals fraction numerator x minus 1 over denominator 4 end fraction$
4y – 196 = 6x – 6
4y = 6x + 190
$y equals fraction numerator 6 x over denominator 4 end fraction plus 190 over 4 equals 3 over 2 x plus 95 over 2$

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